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Mathematics > Numerical Analysis

arXiv:2210.13115 (math)
[Submitted on 24 Oct 2022]

Title:Non-conforming interface conditions for the second-order wave equation

Authors:Gustav Eriksson
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Abstract:Imposition methods of interface conditions for the second-order wave equation with non-conforming grids is considered. The spatial discretization is based on high order finite differences with summation-by-parts properties. Previously presented solution methods for this problem, based on the simultaneous approximation term (SAT) method, have shown to introduce significant stiffness. This can lead to highly inefficient schemes. Here, two new methods of imposing the interface conditions to avoid the stiffness problems are presented: 1) a projection method and 2) a hybrid between the projection method and the SAT method. Numerical experiments are performed using traditional and order-preserving interpolation operators. Both of the novel methods retain the accuracy and convergence behavior of the previously developed SAT method but are significantly less stiff.
Comments: 17 pages, 1 figure. Submitted to Journal of Scientific Computing 29 May 2022
Subjects: Numerical Analysis (math.NA)
MSC classes: 65M06
ACM classes: G.1.8
Cite as: arXiv:2210.13115 [math.NA]
  (or arXiv:2210.13115v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2210.13115

Submission history

From: Gustav Eriksson [view email]
[v1] Mon, 24 Oct 2022 11:05:59 UTC (48 KB)
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